Convolvulus is synonymous with bindweed that grows in poor soil and is notably hard to eradicate. However there are some species of Convovulus that are worth a space in a Mediterranean style garden.

Convolvulus cneorum is a compact evergreen shrub with narrow, oblong, silvery leaves. The numerous flowers are funnel-shaped white flushed with pink when in bud.
Grow in well-drained soil or gritty compost in a sheltered spot in full sun.
The plants are not frost hardy.

Convolvulus White Ensign (Flash Seeds) is a dwarf Morning Glory with clusters of white, trumpet flowers with yellow centres!

Convolvulus Eneorum will withstand a north facing or east facing wall but also dislikes heavy frost. The grey leaved shrubs can grow to 3 foot high and wide.

Resources

Organic Control of Bindweed

Weedkillers for Bindweed

Roundup Weedkiller concentrate

Handy spray gun,